The problem asks us to find the slope and y-intercept of a line from its graph and then use these to write the equation of the line.

1. Problem Description

The problem asks us to find the slope and y-intercept of a line from its graph and then use these to write the equation of the line.

2. Solution Steps

First, we identify two points on the line. From the graph, the line passes through the points $(0, 11)$ and $(9, 0)$.

The slope $m$ of a line passing through points $(x_1, y_1)$ and $(x_2, y_2)$ is given by the formula:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Using the points $(0, 11)$ and $(9, 0)$, we have $x_1 = 0$, $y_1 = 11$, $x_2 = 9$, and $y_2 = 0$.

Therefore, the slope $m$ is:

$m = \frac{0 - 11}{9 - 0} = \frac{-11}{9}$

So, the slope $m$ is $-\frac{11}{9}$.

The y-intercept is the y-coordinate of the point where the line intersects the y-axis. From the given points, the line intersects the y-axis at $(0, 11)$. Therefore, the y-intercept $b$ is

1

1.

The slope-intercept form of a line is given by:

$y = mx + b$

Plugging in the values for $m$ and $b$, we get:

$y = -\frac{11}{9}x + 11$

3. Final Answer

$y = -\frac{11}{9}x + 11$